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NBS TECHNICAL NOTE 688 




U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards 




Yagi Antenna Design 



NEW BOOK SHELF 



JAN 3 1 1977 



NATIONAL BUREAU OF STANDARDS 

The National Bureau of Standards 1 was established by an act of Congress March 3, 1901. 
The Bureau's overall goal is to strengthen and advance the Nation's science and technology 
and facilitate their effective application for public benefit. To this end, the Bureau conducts 
research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific 
and technological services for industry and government, (3) a technical basis for equity in trade, 
and (4) technical services to promote public safety. The Bureau consists of the Institute for 
Basic Standards, the Institute for Materials Research, the Institute for Applied Technology, 
the Institute for Computer Sciences and Technology, and the Office for Information Programs. 

THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United 
States of a complete and consistent system of physical measurement; coordinates that system 
with measurement systems of other nations; and furnishes essential services leading to accurate 
and uniform physical measurements throughout the Nation's scientific community, industry, 
and commerce. The Institute consists of the Office of Measurement Services, the Office of 
Radiation Measurement and the following Center and divisions: 

Applied Mathematics — Electricity — Mechanics — Heat — Optical Physics — Center 
for Radiation Research: Nuclear Sciences; Applied Radiation — Laboratory Astrophysics 2 
— Cryogenics 2 — Electromagnetics - — Time and Frequency 2 . 

THE INSTITUTE FOR MATERIALS RESEARCH conducts materials research leading to 
improved methods of measurement, standards, and data on the properties of well-characterized 
materials needed by industry, commerce, educational institutions, and Government; provides 
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Analytical Chemistry — Polymers — Metallurgy — Inorganic Materials — Reactor 
Radiation — Physical Chemistry. 

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the use of available technology and to facilitate technological innovation in industry and 
Government; cooperates with public and private organizations leading to the development of 
technological standards (including mandatory safety standards), codes and methods of test; 
and provides technical advice and services to Government agencies upon request. The Insti- 
tute consists of the following divisions and Centers: 

Standards Application and Analysis — Electronic Technology — Center for Consumer 
Product Technology: Product Systems Analysis; Product Engineering — Center for Building 
Technology: Structures, Materials, and Life Safety; Building Environment; Technical Evalua- 
tion and Application — Center for Fire Research: Fire Science; Fire Safety Engineering. 

THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts research 
and provides technical services designed to aid Government agencies in improving cost effec- 
tiveness in the conduct of their programs through the selection, acquisition, and effective 
utilization of automatic data processing equipment; and serves as the principal focus within 
the executive branch for the development of Federal standards for automatic data processing 
equipment, techniques, and computer languages. The Institute consists of the following 
divisions: 

Computer Services — Systems and Software — Computer Systems Engineering — Informa- 
tion Technology. 

THE OFFICE FOR INFORMATION PROGRAMS promotes optimum dissemination and 
accessibility of scientific information generated within NBS and other agencies of the Federal 
Government; promotes the development of the National Standard Reference Data System and 
a system of information analysis centers dealing with the broader aspects of the National 
Measurement System; provides appropriate services to ensure that the NBS staff has optimum 
accessibility to the scientific information of the world. The Office consists of the following 
organizational units: 

Office of Standard Reference Data — Office of Information Activities — Office of Technical 
Publications — Library — Office of International Relations — Office of International 
Standards. 



1 Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address 
Washington. DC. 20234. 

- Located at Boulder. Colorado 80302. 



Yagi Antenna Design 



Peter P. Viezbicke 



Time and Frequency Division 
Institute for Basic Standards 
National Bureau of Standards 
Boulder, Colorado 80302 



*t* T 0F o r 



/ V 









U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary 

Edward 0. Vetter, Under Secretary 

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology 

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director 
Issued December 1976 



NATIONAL BUREAU OF STANDARDS TECHNICAL NOTE 688 
Nat. Bur. Stand. (U.S.), Tech Note 688, 27 pages (December 1976) 

CODEN: NBTNAE 



U.S. GOVERNMENT PRINTING OFFICE 
WASHINGTON: 1976 



For sale by the Superintendent of Documents, US Government Printing Office, Washington, DC. 20402 
(Order by SD Catalog No. C13. 46:688) Price 65 cents (Add 25 percent additional for other than U.S. mailinj 



FOREWORD 



This work was carried out by the National 
Bureau of Standards at antenna test ranges 
located in Sterling, Virginia, and at Table 
Mountain near Boulder, Colorado. 

These measurements were carried out by the 
Antenna Research Section of the Radio System 
Division, National Bureau of Standards. 



I i 



CONTENTS 



1. INTRODUCTION 

2. METHOD OF MEASUREMENT 

3. RESULTS 

3.1 Effect of Reflector Spacing on Measured Gain 

3.2 Effect of Different Equal Length Directors and 
for Different Yagi Lengths 



Spac 



ng on Measured 



Gain 



3.3 Effect of Different Diameters and Lengths of Directors on Measured Gain 

3.4 Effect of the Size of a Supporting Boom on the Optimum Length of a 
Parasitic Element .......... 

3.5 Effect of Spacing and Stacking of Yagi Antennas on Realizable Gain 

3.6 Measured Radiation Patterns of Different Length Yagi Antennas 
k. DESIGNING THE YAGI ANTENNA 

5. CONCLUSIONS 

6. ACKNOWLEDGMENTS .... 

7. REFERENCES 



Page 
1 

1 
1 
2 



6 
6 
6 
16 
21 
21 
21 



LIST OF TABLES and FIGURES 



Table 1. Optimized Lengths of Parasitic Elements for Yagi Antennas of Six 
Different Lengths .......... 

Figure 1. Gain in dB of a Dipole and Reflector for Different Spacings Between 
Elements ........... 

Figure 2. Arrangement of Three Reflecting Elements Used With the k.2X Yagi 

Figure 3. Photograph of the Trigonal Reflector Experimental Set-Up Used With 
the k.2\ Yagi 

Figure k. Gain of a Yagi as a Function of Length (Number of Directors) for 
Different Constant Spa. igs Between Directors of Length Equal to 
0.382X . 

Figure 5- Gain of a Yagi as a Function of Length (Number of Directors) for 
Different Constant Spacings Between Directors of Length Equal to 
0.41 U . 

Figure 6. Gain of a Yagi as a Function of Length (Number of Directors) for 
Different Constant Spacings Between Directors of Length Equal to 
O.klkX .-..." 



Figure 7. 

Figure 8. 

Figure 9- 

Figure 10. 
Figure 1 1 . 

Figure 12. 

Figure 13. 
Figure ]k. 
Figure 15. 
Fi gure 16. 
Figure 17. 
Figure 18. 
Figure 19. 
Figure 20. 

Figure 21 , 



Comparison of Gain of Different Length Yagis Showing the Relationship 
Between Directors Optimized in Length to Yield Maximum Gain and 
Directors of Optimum Uniform Length ....... 

Measured Gain Vs Director Length of a 1.25A Yagi Antenna Using Three 
Directors of Different Length and Diameter Spaced 0.35A. 

Yagi Antenna Design Data Showing the Relationship Between Element 
Diameter to Wavelength Ratio and Element Length for Different Antennas 



Graph Showing the Effect of a Supporting Boom on Length of Elements 

Gain of an Array of Yagis, Stacked One Above the Other and in Broads 
as a Function of Spacing ...... 

Gain of an Array of Two Sets of Stacked Yagis Spaced 1 .6X as a funct 
of Horizontal Distance Between Them ..... 

Radiation Patterns of a Dipole and Reflector With 0.2A Spacing 

Radiation Patterns of a 3~Element, 0.k\ Long Yagi 

Radiation Patterns of a 5-Element, 0.8A Long Yagi 

Radiation Patterns of a 6-Element, 1.2A Long Yagi 

Radiation Patterns of a 12-Element, 2.2X Long Yagi 

Radiation Patterns of a 17-Element, 3.2X Long Yagi 

Radiation Patterns of a 15 - Element, 4.2X Long Yagi 

Use of Design Curves in Determining Element Lengths of 0.8X Yag 
Considered in Example 1 ....... 

Use of Design Curves in Determining Element Lengths of h.2X Yag 
Considered in Example 2 ....... 



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20 



VI 



YAGI ANTENNA DESIGN 
Peter P. Viezbicke 

This report presents data, using modeling techniques, for the optimum design 
of different length Yagi antennas. This information is presented in graphical 
form to facilitate the design of practical length antennas--f rom 0.2A to k.2X 
long--for operation in the HF, VHF, and UHF frequency range. The effects of 
different antenna parameters on realizable gain were also investigated and the 
results are presented. Finally, supplemental data are presented on the stacking 
of two or more antennas to provide additional gain. 

Key words: Antenna, director, driven element, gain, radiation pattern, reflector, 
Yagi. 

1 . INTRODUCTION 

The Yagi-Uda antenna [1], commonly known as the Yagi, was invented in 1926 by Dr. H. Yagi 
and Shintaro Uda. Its configuration normally consists of a number of directors and reflectors 
that enhance radiation in one direction when properly arranged on a supporting structure. 

Since its discovery, a large number of reports have appeared in the literature relative 
to the analysis, design, and use of the Yagi antenna [2, 3, 4, 5, 6, 7, 8, 9], However, 
little or no data seem to have been presented regarding how parasitic element diameter, 
element length, spacings between elements, supporting booms of different cross sectional 
area, various reflectors, and overall length affect measured gain. 

This report presents the results of extensive measurements carried out by the National 
Bureau of Standards to determine these effects and gives graphical data to facilitate the 
design of different length antennnas to yield maximum gain. In addition, design criterion 
is also presented on stacki ng--one above the other and in a columnar configuration. The 
gain is given in decibels (dB) relative to a dipole (reference antenna) at the same height 
above ground as the test (Yagi) antenna. 

2. METHOD OF MEASUREMENT 



The measurements were carried out at the NBS antenna range when it was located at 
Sterling, Virginia, and at Table Mountain, Colorado, after the antenna research group was 
relocated to Colorado. All measurements were conducted at a modeling frequency of 400 MHz. 
The antenna under test was used as a receiving antenna and was located approximately 
320 meters from a target transmitter and antenna. The transmitting antenna was located at 
a height above ground so that the receiving antennas were illuminated at grazing angles. 
The Yagi under test was mounted 3^ (wavelength) above ground and its gain was compared to 
a reference dipole antenna located approximately 5A to one side and at the same height as 
the test antenna. Each antenna was matched precisely to 50 ohms and switched alternately 
to an attenuator and associated receiving and detecting equipment located in a nearby 
wooden building. In comparing the attenuator readings of the two antennas to produce a 
constant receiver output level, line losses to each were measured and compensated for in 
arriving at final values of gain. The values of gain were reproducible to within 0.2 dB 
over the period when measurements were being carried out. The values presented are those 
measured in a forward direction compared to the maximum response of a dipole at the same 
height above ground and are believed accurate to within 0.5 dB. If referenced to an 
isotropic source, the values must be increased by 2.16 dB. 

3. RESULTS 



The results of the measurements carried out in this study are presented in graphical 
form. They are intended to provide a simple means of designing a Yagi antenna of practical 
dimensions with maximum gain for the configuration under consideration. The purpose of 
these tests was to determine the following: 



a. Effect of reflector spacing on the gain of a dipole antenna 

b. Effect of different equal length directors, their spacing and number on 
real izable gai n 

c. Effect of different diameters and lengths of directors on realizable gain 

d. Effect of the size of a supporting boom on the optimum length of parasitic 
el ements 

e. Effect of spacing and stacking of antennas on gain 

f. Measured radiation patterns of different Yagi configurations 

3.1 EFFECT OF REFLECTOR SPACING ON MEASURED GAIN 

These tests as well as all others were carried out on a non-conducting plexiglass 
boom mounted 3A above ground. With the exception of measurements stated in sections 3.3 
and 3-^, all parasitic elements were constructed of 0.63 cm (one-fourth inch) diameter 
aluminum tubing. The driven element used in the Yagi as well as in the reference dipole 
was a half-wave folded dipole matched to 50 ohms using a double-stub tuner. 

The gain of a dipole and reflector combination for different spacings between the two 
elements is shown in figure 1. Maximum measured gain was 2.6 dB and was realized at a 
spacing of 0.2A behind the dipole. This reflector spacing was used in all subsequent 
measurements. However, for the different Yagi configurations the reflector length was 
optimized to yield maximum gain. An additional 0.75 dB gain was realized using the 
reflector configuration shown in figure 2. 

Although this arrangement was used only on the ^4 . 2X long Yagi, comparable benefits 
would be realized with other antenna lengths. A photograph of the experimental set-up for 
this configuration is shown in figure 3. 

Various arrangements and spacings of reflector elements were tested on the k.2\ Yagi 
using the drilled plexiglass support as shown. The reflecting elements were arranged in 
shapes of plane reflecting surfaces, parabolas and corner reflectors. In addition, 
different shaped solid reflecting surfaces placed at various distances behind the driven 
element were also used. Of the combinations tested, the one shown in figure 2 yielded the 
largest increase in gain over that of the single reflecting element. 

3.2 EFFECT OF DIFFERENT EQUAL LENGTH DIRECTORS AND 

SPACING ON MEASURED GAIN FOR DIFFERENT YAGI LENGTHS 



These measurements were conducted using the same non-conducting boom as mentioned in 
the preceding section. The driven element consisted of a A/2 folded dipole; the reflector 
was 0.^82X in length and spaced 0.2A behind the driven element. The diameter of all 
elements was 0.0085A '(0.25 inches = 0.63cm). 

The gain of the Yagi was measured as a function of antenna length (number of directors] 
for different equal length directors and spacing between them. The director lengths were 
varied from 0.304A to 0.423A and spacings from 0.01A to 0.40X. The Yagi length, measured 
from the driven element to the last director, was varied from an overall length of 0.2A to 
10. 2X. The reflector in all cases was fixed. Although many measurements were carried out, 
only those results and associated graphs are presented that show the effects of these 
parameters on measured gain. 

Figures k, 5, and 6 show the relative gain of a Yagi as a function of length for 
different spacings between director elements using director lengths of 0.382A, 0.^1 IX, 
and O.kmX. Figure h shows that for relatively short directors at a spacing of 0.3X, 
the gain of the Yagi increased to a maximum value of 14.5 dB when the antenna length was 
increased to approximately 10A. Note, however, that as the spacing between elements was 



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.05 .10 .15 .20 .25 .30 .35A 
SPACING, S, OF REFLECTOR BEHIND DRIVEN ELEMENT 

FIG. 1 GAIN IN dB OF A DIPOLE AND REFLECTOR FOR 
DIFFERENT SPACINGS BETWEEN ELEMENTS 



0.173A 



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LR3 il 



0.135A 



DIRECTORS 



DRIVEN 
ELEMENT 




® 

LR3 



0.27X 



REFLECTOR LENGTHS 

LR1 = LR2 = 0.455A 
LR3 = 0.473A 
FREQ = 400 MHz 



[LENGTHS NOT CORRECTED FOR BOOM OR SUPPORT THICKNESS] 



©' 



LR2 



FIG. 2 ARRANGEMENT OF THREE REFLECTING ELEMENTS USED WITH THE 4.2X YAG I 




FIG. 3 PHOTOGRAPH OF THE TRIGONAL REFLECTOR EXPERIMENTAL 
SET-UP USED WITH THE k . 2\ YAG I 



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0.3A SPACING 



°- 0.4A SPACING 



0.2X SPACING 

0.06A SPACING 
0.10X SPACING 



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ADD 0.2X 
FOR REFL 



2 3 4 5 6 7 
LENGTH OF YAGI IN WAVELENGTHS 



FIG. k GAIN OF A YAGI AS A FUNCTION OF LENGTH (NUMBER OF DIRECTORS) 
FOR DIFFERENT CONSTANT SPACINGS BETWEEN DIRECTORS OF LENGTH 
EQUAL TO 0.382X 



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ADD 0. 2X 

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2 3 4 5 6 7 
LENGTH OF ANTENNA IN WAVELENGTHS 



3X SPACING 



0.4A SPACING 



FIG. 5 GAIN OF A YAG I AS A FUNCTION OF LENGTH (NUMBER OF DIRECTORS', 
FOR DIFFERENT CONSTANT SPACINGS BETWEEN DIRECTORS OF LENGTH 
EQUAL TO 0.*tl U 



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ADD 0.2A 
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2 3 4 5 6 7 
LENGTH OF ANTENNA IN WAVELENGTHS 



0.30X SPACING 



FIG. 6 GAIN OF A YAG I AS A FUNCTION OF LENGTH (NUMBER OF DIRECTORS) 
FOR DIFFERENT CONSTANT SPACINGS BETWEEN DIRECTORS OF LENGTH 
EQUAL TO O.klkX 



decreased, an oscillatory wave pattern resulted wherein the maximum gain occurred at a 
shorter Yagi length and varied between a maximum and minimum value as the length of the Yag i 
was changed. As the length of the directors was increased, the variations in the wave 
pattern were also enhanced together with a reduction in gain as shown in figures 5 and 6. 

The curves presented in figure 7 show a comparison of realized gain vs Yagi length up 
to k .2\ for antennas using directors of equal length and those optimized in length. For the 
optimized length configurations the gain increased from 0.5 dB for the 2.2A. antenna to 
approximately 1.5 dB for the 4.2A Yagi. Table 1 gives details of antenna parameters for the 
different optimized design lengths tested and measured. 

3.3 EFFECT OF DIFFERENT DIAMETERS AND LENGTHS OF DIRECTORS ON MEASURED GAIN 

This effect was determined by measuring the gain of different Yagi configurations for 
different director lengths of various diameters. Curves showing the results of measurements 
carried out on the 1.25A long Yagi are given in figure 8. As expected, the maximum gain for 
the different combinations remained unchanged. The larger diameter elements yielded maximum 
gain at shorter lengths while the smaller diameter elements yielded maximum gain at corre- 
spondingly greater lengths. Results of a series of measurements, noting these effects, were 
carried out on the different length Yagis and, together with results presented in Table 1, a 
set of design curves was produced and is presented in figure 9- These data provide the 
basic design criterion of the Yagi antenna and are valid over a large frequency range provided 
the selected element diameter to wavelength ratio d/X falls within the limits shown. 

3. it EFFECT OF THE SIZE OF A SUPPORTING BOOM ON 
THE OPTIMUM LENGTH OF A PARASITIC ELEMENT 

Round and square supporting booms of different cross-section area were employed in 
Yagi antennas of different lengths to determine what effect the boom diameter had on the 
optimum length of the parasitic elements. The round and square booms yielded similar 
results. The effect of a round supporting boom on the length of a parasitic element is 
represented by the curve in figure 10. This experimental response can be used in applying 
the boom correction for the final Yagi design. 

3.5 EFFECT OF SPACING AND STACKING OF YAGI ANTENNAS ON REALIZABLE GAIN 

As shown in figure 11, additional gain is realized when antennas are stacked one 
above the other or in broadside. Not only is gain increased but the beamwidth is reduced 
appreciably depending upon the configuration employed. 

Figure 11 (A) shows the effects of stacking two antennas, one above the other. These 
responses show similar mutual effects between two seven-element Yagis and between two 
fifteen-element Yagis. At close spacing, approximately 0.8A, the gain was reduced due to 
high mutual impedance effects but increased to a maximum of 2.5 dB as the spacing was 
increased to approximately 1.6A. Similar effects were measured with the combination shown 
in figure 11 (B) . Maximum gain in this case was realized with the two antennas spaced at 
approximately 2.0A. 

A combination of the above two configurations using spacings as shown yielded an 
additional 2.5 dB gain and a corresponding reduction in beamwidth. For example, four 0.8A 
Yagi antennas, appropriately stacked, spaced and fed in phase yielded a gain of 1^.2 dB 
relative to a dipole located at the same height above ground. In contrast, a combination 
of four 4.2A Yagi antennas yielded a gain of 19-6 dB relative to a dipole, as shown by the 
graph in figure 12. 

3.6 MEASURED RADIATION PATTERNS OF DIFFERENT LENGTH YAGI ANTENNAS 

Radiation patterns measured in the E (hor i zontal -sol id curves) and H (vert ical -dashed 
curves) planes for different Yagi designs are presented in figures 13 through 19. The 
radiation patterns of the simplest yagi array (which consists of a reflector and driven 



TABLE 1. OPTIMIZED LENGTHS OF PARASITIC ELEMENTS 
FOR YAGI ANTENNAS OF SIX DIFFERENT LENGTHS 







LENGTH OF YAGI IN WAVELENGTHS 




0.4 0.8 

i 


1 .20 


2.2 


3-2 


4.2 


LENGTH OF 
REFLECTOR, A 


0.482 


0.482 


0.482 


0.482 


0.482 


0.475 


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1st 


0.424 


428 


0.428 


0.432 


0.428 


0.424 


2nd 




0.424 


0.420 


0.415 


0.420 0.424 


3rd 




0.428 


0.420 


0.407 


0.407 0.420 


4th 






0.428 


0.398 


0.398 J 0.407 


5th 








0.390 


0.394 


0.403 


6th 








0.390 


0.390 


0.398 


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7th 








0.390 0.386 


0.394 




8th 








0.390 


0.386 


0.390 


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9th 








0.398 


O.386 


0.390 


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0.407 


0.386 


0.390 


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11th 

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O.386 


0.390 


12th 




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0.386 


0.390 


13th i 

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O.386 


0.390 


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O.386 




15th 










O.386 




SPACING BETWEEN 
DIRECTORS, IN A 


0.20 


0.20 


0.25 


0.20 


0.20 


0.308 

! 


GAIN RELATIVE 
TO HALF-WAVE 
DIPOLE IN dB 


7.1 


9.2 


10.2 


12.25 


13.4 


14.2 


DESIGN CURVE ! , v 
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f = 400 MHz 
REFLECTOR SPACED C.2A BEHIND DRIVEN ELEMENT 



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FOR MAXIMUM GAIN (SEE TABLE 1) 

© DIRECTORS OF OPTIMUM UNIFORM LENGTH 




N = NUMBER OF DIRECTORS 

S = SPACING BETWEEN DIRECTORS 

(REFLECTOR SPACED 0. 2A ON ALL ANTENNAS) 



1.0 2.0 3.0 4.0 

OVERALL LENGTH, IN WAVELENGTHS, OF DIFFERENT YAG I S 



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FIG. 7 COMPARISON OF GAIN OF DIFFERENT LENGTH YAG I S SHOWING THE 

RELATIONSHIP BETWEEN DIRECTORS OPTIMIZED IN LENGTH TO YIELD 
MAXIMUM GAIN AND DIRECTORS OF OPTIMUM UNIFORM LENGTH 



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LENGTH OF DIRECTORS IN INCHES 



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FIG. 8 MEASURED GAIN VS DIRECTOR LENGTH OF A 1.25X YAG I ANTENNA 
USING THREE DIRECTORS OF DIFFERENT LENGTH AND DIAMETER 
SPACED 0.35X 



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7 ELEMENT YAGI ANTENNAS 
15 ELEMENT YAGI ANTENNAS 



(A) VERTICAL SPACING, S IN WAVELENGTHS, BETWEEN ANTENNAS 



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-o- 7 ELEMENT YAGI ANTENNAS 
--•-15 ELEMENT YAGI ANTENNAS 

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(B) HORIZONTAL SPACING, S IN WAVELENGTHS, BETWEEN ANTENNAS 

FIG. 11 GAIN OF AN ARRAY OF YAG I S , STACKED ONE ABOVE THE OTHER 
AND IN BROADSIDE, AS A FUNCTION OF SPACING 



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FIG. 19 RADIATION PATTERNS OF A 15-ELEMENT, k.2\ LONG YAG 



15 



element) are presented in figure 13. The 3~dB E and H plane beamwidths measured 66 and 
111° respectively. The beamwidth of the 3-element . ^X antenna, as shown in figure 1 4 , 
measured 57 and 72 in the E and H planes respectively. The E plane, front-to-side ratio 
is in the order of 24 dB, while the radiation to the rear was only 8 dB down from that in 
the forward direction. 

The radiation pattern of the 5 _ element 0.8A Yag i presented in figure 15 is characterized 
by a 3 dB beamwidth of 48 and 56 in the E and H planes respectively. The E plane, 
front-to-side ratio remained comparable to the 3 - element antenna; however, the front-to- 
back ratio was improved considerably and measured 15 dB. In radiation patterns of 6, 12, 
17 and 15-element Yagis as shown in figures 16 through 19, the beamwidths became progres- 
sively smaller as was expected with increased gain. 

4. DESIGNING THE YAG I ANTENNA 

To facilitate the design of an antenna of practical dimensions and yet realize maximum 
gain, refer to the curves shown in figure 9- These data were developed from results of 
model measurements carried out at 400 MHz using elements of different diameters. Only 
those curves are presented which will enable the user to design the 0.4, 0.8, 1.2, 2.2, 
3.2 and 4.2A long Yagis that yield gains of 7.1, 9-2, 10.2, 12.3, 13.4 and 14.2 dB respec- 
tively over that of a dipole mounted at the same height above ground. 

In designing a Yag i antenna, the following basic information is required and, of 
course, will depend upon individual requirements. 

1. Frequency of operation, f (wavelength, A) 

2. Antenna gain required, G (dB) 

3. Diameter of parasitic elements (directors-reflectors) used in construction, d/A 

4. Diameter of supporting boom used in construction, D/A 

Careful consideration should also be given to selection of the diameter of the 
elements and boom at the wavelength or frequency of operation. This is important since 
smaller diameter and lighter materials can be used at the higher frequencies in contrast 
to larger and heavier materials needed for support at the lower frequencies. Note also 
that the selected element diameter-to-wavelength ratios used in the design of the chosen 
antenna must fall within the limits shown. 

If maximum gain is to be realized using the data presented, it is essential to follow 
very closely the procedure described here. In addition, the element lengths should be 
measured and cut to a tolerance of about 0.003A with respect to the calculated values. To 
aid the user in the design of this antenna and to familiarize him in use of the design 
data, two specific examples are presented. The first considers the design of a 5 - element, 
0.8A Yagi; the second example presents a step-by-step procedure for the design of a 15- 
element, 4.2A Yagi. In the first example, consider the design of a 0.8A Yagi antenna to 
operate at a frequency of 50.1 MHz in the amateur radio band and yield a gain of 9-2 dB 
relative to a dipole. The elements shall be constructed of 2.54 cm (1 in.) diameter 
aluminum tubing with the boom of 5.08 cm (2 in.) diameter aluminum tubing. 

GIVEN: Frequency 50.1 MHz, A = 597 cm. (235 in.) 

Element Diameter, d = 2.54 cm. (1 in.) 

d/A = 0.0042 

Boom diameter, D = 5.1 cm. (2 in.) 

D/A = 0.0085 

Element spacing = 0.2A = 119 cm. (47 in.) 

Overall length - 0.8A = 478 cm. (188 in.) 



16 



STEP 1: Plot the lengths of the parasitic elements obtained from Table 1 for 0.8X long 
Yagi on the corresponding curve in figure 9. For clarity, these curves are 
reproduced in figure 20. Establish points L = L_ , L,, , L D and determine 

the parasitic element lengths for d/A = 0.0085. 

Thus L = L - 0.428A 
1 3 

L = 0.424A 
U 2 

L Q = 0.482A 
K 

STEP 2: For our design, where the element diameter to wavelength ratio d/A = 0.0042, 

plot and establish this point on the director curve and indicate by a check 

mark (/) . This is the uncompensated director length of D. = D = 0.442A. 

STEP 3= For the same d/A ratio, determine the uncompensated length of the reflector 

L D = 0.485A. 
K 

STEP h: With a pair of dividers, measure the distance along the curve between the initial 

points D. = D, to D determined in Step 1. Transpose this distance from the 

point established in Step 2 downward along the curve and determine the uncom- 
pensated length of director L = 0.438A. 

2 

From the foregoing, the uncompensated parasitic element lengths for the 50.1 MHz 
Yagi are: 

L = 0.438A 
2 

L D = 0.485A 
K 

To these values, a correction must be added to compensate for the boom diameter. 
STEP 5: Refer to figure 10. For a boom diameter-to-wavelength ratio D/A = 0.0085, 
determine the fractional increase in wavelength by which each of the para- 
sitic elements must be increased. From the chart this length = 0.005A. 
Thus, for this design the exact lengths of the parasitic elements should be 
measured and cut to the following lengths. 

L = L = Q.hklX + 0.005A = 0.^7A = 267 cm. 
1 3 

L = 0.438A + 0.005A = 0.443A = 264. 5 cm. 
2 

= 0.485A + 0.005A = 0.490A = 293 cm. 
R 

The driven element is designed so that the Yagi can work either into a 50 or 200 ohm load 
impedance. For a 50 ohm impedance, a folded dipole and a quarter-wave balun can be employed. 
Precise matching to 50 ohms can be accomplished by using a double-stub tuner connected into 
the feed 1 ine. 



17 









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If the antenna is designed with a 200 ohm balanced input impedance, then the driven 
element should be designed to provide an impedance step-up ratio of 12. For this configura- 
tion, a A/2 balun section and stubs can be used to provide proper impedance transformation 
and matching. Other matching methods can also be employed such as Gamma or T match [10, 11, 
12]. 

As a second example, consider the design of a k .2\ long Yagi to provide a gain of 1^.2 
dB relative to a dipole to operate on 827 MHz in the center of TV Channel 73. For the 
construction of this antenna let us select and use a 1/2-inch diameter boom with 3/1 6- i nch 
diameter elements using thin wall brass tubing. 

GIVEN: Frequency 827 MHz, A = 36. 3*+ cm. (1^.3 in.) 

Element diameter, d = 0.48 cm. 

d/A = 0.013 

Boom diameter, D = 1 .27 cm. (1/2 in.) 

D/A = 0.035 

Element spacing = 0.308A = 11.2 cm. 

Overall length - 4.2A = 152 cm. 
STEP 1: Plot the lengths of parasitic elements from Table 1 for the 4.2A long Yagi on 

the corresponding curve in figure 9. For clarity, these curves are reproduced 

and presented in fiqure 21. Establish points L^ = L^ , L„ ...L„ and locate 

D, D 2 D 3 D 13 

the parasitic element lengths on the curve as in the previous example for the 
d/A = 0.0085 case. 

STEP 2: For our particular design, however, where the element diameter to wavelength 
ratio d/A = 0.013, plot and establish this point on the 4.2A long Yagi curve 
and indicate this starting point with a check (/) . This is the uncompensated 
director length of D = D = 0.414A.. 

STEP 3: For the same d/A ratio, determine the uncompensated length of the reflector, 

L D = 0.473A; from curve D, figure 21. 
K 

STEP k: With the use of a pair of dividers, establish and measure the distance be- 
tween the points D. = D„ to D_. Transpose this distance from the initial (/) 

mark downward along the director curve and determine L = 0.409A. 

Measure the distance from D, = D„ to D,. Transpose this distance from 

initial (/) point and determine length of D, = 0.395A. Similarly, 

determine remaining director lengths. L = 0.391A, L = O.385A, L = 

U 5 6 U 7 

0.381A, L. to L n = 0.377A. 
U 8 U 13 

To these values a correction must be added to compensate for boom diameter. 

STEP 5: Again, refer to figure 10. For a boom diameter-to-wavelength ratio D/A = 

0.035, determine the fractional amount by which each element must be 

increased to compensate for boom. From the curve, determine this length = 

0.026A. 

Thus, to realize maximum gain from this antenna, measure and cut the 

parasitic elements to the following lengths: 

19 



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20 



L = L = .41 ^tX + 0.026A = 0.440A = 16.0 cm. 
1 2 

L = 0.409A + 0.026A = 0.435A = 15-8 cm. 

L n = 0.395A + 0.026A = .421 X = 15-3 cm. 
U 4 

L n = 0. 391 X + 0.026A = 0.417A = 15.1 cm. 
5 

L = 0.385X + 0.026A = 0.41 IX = 14.9 cm. 
D 6 

L = 0.381A + 0.026A = 0.407A = 14.8 cm. 

7 

L - L = 0.377A + 0.026A = 0.403A = 14.6 cm. 

D 8 D 13 

L D = 0.473A + 0.026A = 0.499A = 18.1 cm. 
R 

The driven element can be of a variety of designs and will depend upon 

individual requirements. It is usually measured and cut to one-half 

wavelength less a shortening factor to compensate for end-effects and 

matched to the characteristic impedance of the feed line. 

5. CONCLUSIONS 

The data presented in this report provide the necessary information for the design of 
Yagi antennas ranging in length from 0.2A to 4.2A. These data allow the user to design 
antennas to yield maximum gain for seven different design configurations. In addition, 
stacking of antennas, side by side and one above the othei — all fed in phase — provides an 
additional gain up to 5.2 dB over that of the single array. 

6. ACKNOWLEDGMENTS 

The author wishes to extend sincere appreciation to William Gorboczieski for his assist- 
ance in the fabrication of test set-ups and in carrying out of the measurements. Also, 
sincere appreciation and thanks to Alvin Wilson for providing the radiation patterns. 

7. REFERENCES 



[1] Shintaro, U., and Yasuto, M. , Yagi-Uda Antennas (Sasoki Printing and Publishing Co., 
Ltd., Senda, Japan, 1954). 

[2] Mailloux, R. J., The long Yagi-Uda array, IEEE, Trans. Antennas and Prop., AP-1 4 , 
pp. 128-137 (Mar. 1966). 

[3] Barbano, N. , Log periodic Yagi-Uda array, IEEE, Trans. Antennas and Prop., AP-1 4 , 
pp. 235-238 (Mar. 1966). 

[4] Thiele, G. A., Analysis Y Yagi-Uda type antennas, IEEE, Trans. Antennas and Prop. AP-1 7 , 
pp. 24-31 (Jan. 1 969) . 

[5] Emerson, J., Arranging Yagi antennas for positive results, Broadcast Engineering, No. 5, 
pp. 32-40 (May 1971). 

[6] Shen, L., Directivity and bandwidth of single-band and double band Yagi arrays, IEEE, 
Trans. Antennas and Prop., AP-20, pp. 178-I8O (Nov. 1972). 



21 



[7] Cheng, D. K. , and Chen, C. A., Optimum element spacings for Yagi-Uda arrays, IEEE, Trans 
Antennas and Prop., AP-21 , pp. 615-623 (Sept. 1973). 

[8] Chen, C. A., and Cheng, D. K. , Optimum element lengths for Yagi-Uda arrays, IEEE, Trans. 
Antennas and Prop., AP-23 , pp. 8-15 (Jan. 1975). 

[9] Nose, K. , Crossed Yagi antennas for circular polarization, QST, pp. 21-24 (Jan. 1973). 

[10] Healey, D. J., Ill, An examination of the Gamma Match, QST, pp. 11-15 (Apr. 1969). 

[11] Nose, K. , Adjustment of Gamma-matched parasitic beams, QST, pp. kk-hS (Mar. 1958). 

[12] The Radio Amateur's Handbook, Fifty Second Ed. (AM Radio Relay League, 1976). 



22 



m^mi^^ 



U.S. DEPT. OF COMM. 

Er.BLIOGRAPHIC DATA 
SHEET 



1. PUBLICATION OR REPORT NO. 

NBS-TN-688 



2. Gov't Accession 
No. 



4. TITLE AND SUBTITLE 



YAGI ANTENNA DESIGN 



3. Recipient's Accession No. 



5. Publication Date 



December 1976 



6. Performing Organization Code 

277.00 



7. AUTHOR(S) 



Peter P. Viezbicke 



8. Performing Organ. Report No. 



9. PERFORMING ORGANIZATION NAME AND ADDRESS 

NATIONAL BUREAU OF STANDARDS 
DEPARTMENT OF COMMERCE 
WASHINGTON, D.C. 20234 



10. Project/Task/Work Unit No. 

2776124 



11. Contract/Grant No. 



12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP) 



Same as 9. 



13. Type of Report & Period 
Covered 

FINAL 



14. Sponsoring Agency Code 



15. SUPPLEMENTARY NOTES 



16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant 
bibliography or literature survey, mention it here.) 

This report presents data, using modeling techniques, for the optimum design of 
different length Yagi antennas. This information is presented in graphical form to 
facilitate the design of practical length antennas--from 0.2A to 4.2A long--for 
operation in the HF, VHF, and UHF frequency range. The effects of different 
antenna parameters on realizable gain were also investigated and the results are 
presented. Finally, supplemental data are presented on the stacking of two or more 
antennas to provide additional gain. 



17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper 
name; separated by semicolons) 

Antenna, director, driven element, gain, radiation pattern, reflector, Yagi. 



18. AVAILABILITY IXX Unlimited 

~2 For Official Distribution. Do Not Release to NTIS 

)CX ! Order From Sup. of Doc, U.S. Government Pruitine Office 
Washington, D.C. 20402, SD Cat. No. C13 -46 ! 688 

J Order From National Technical Information Service (NTIS) 
Springfield, Virginia 22151 



19. SECURITY CLASS 
(THIS REPORT) 



UNCLASSIFIED 



20. SECURITY CLASS 
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21. NO. OF PAGES 



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work at NBS. The magazine highlights and reviews 
such issues as energy research, fire protection, building 
technology, metric conversion, pollution abatement, 
health and safety, and consumer product performance. 
In addition, it reports the results of Bureau programs 
in measurement standards and techniques, properties of 
matter and materials, engineering standards and serv- 
ices, instrumentation, and automatic data processing. 

Annual subscription: Domestic, $9.45; Foreign, $11.85. 

NONPERIODICALS 

Monographs — Major contributions to the technical liter- 
ature on various subjects related to the Bureau's scien- 
tific and technical activities. 

Handbooks — Recommended codes of engineering and 
industrial practice (including safety codes) developed 
in cooperation with interested industries, professional 
organizations, and regulatory bodies. 
Special Publications — Include proceedings of conferences 
sponsored by NBS, NBS annual reports, and other 
special publications appropriate to this grouping such 
as wall charts, pocket cards, and bibliographies. 
Applied Mathematics Series — Mathematical tables, man- 
uals, and studies of special interest to physicists, engi- 
neers, chemists, biologists, mathematicians, com- 
puter programmers, and others engaged in scientific 
and technical work. 

National Standard Reference Data Series — Provides 
quantitative data on the physical and chemical proper- 
ties of materials, compiled from the world's literature 
and critically evaluated. Developed under a world-wide 
program coordinated by NBS. Program under authority 
of National Standard Data Act (Public Law 90-396). 



NOTE: At present the principal publication outlet for 
these data is the Journal of Physical and Chemical 
Reference Data (JPCRD) published quarterly for NBS 
by the American Chemical Society (ACS) and the Amer- 
ican Institute of Physics (AIP). Subscriptions, reprints, 
and supplements available from ACS, 1155 Sixteenth 
St. N.W., Wash. D. C. 20056. 

Building Science Series — Disseminates technical infor- 
mation developed at the Bureau on building materials, 
components, systems, and whole structures. The series 
presents research results, test methods, and perform- 
ance criteria related to the structural and environmental 
functions and the durability and safety characteristics 
of building elements and systems. 

Technical Notes— Studies or reports which are complete 
in themselves but restrictive in their treatment of a 
subject. Analogous to monographs but not so compre- 
hensive in scope or definitive in treatment of the sub- 
ject area. Often serve as a vehicle for final reports of 
work performed at NBS under the sponsorship of other 
government agencies. 

Voluntary Product Standards — Developed under proce- 
dures published by the Department of Commerce in Part 
10, Title 15, of the Code of Federal Regulations. The 
purpose of the standards is to establish nationally rec- 
ognized requirements for products, and to provide all 
concerned interests with a basis for common under- 
standing of the characteristics of the products. NBS 
administers this program as a supplement to the activi- 
ties of the private sector standardizing organizations. 
Consumer Information Series — Practical information, 
based on NBS research and experience, covering areas 
of interest to the consumer. Easily understandable lang- 
uage and illustrations provide useful background knowl- 
edge for shopping in today's technological marketplace. 

Order above NBS publications from: Superintendent 
of Documents, Government Printing Office, Washington, 
D.C. 20402. 

Order following NBS publications — NBSIR's and FIPS 
from the National Technical Information Services, 
Springfield, Va. 22161. 

Federal Information Processing Standards Publications 
(FIPS PUBS) — Publications in this series collectively 
constitute the Federal Information Processing Stand- 
ards Register. Register serves as the official source of 
information in the Federal Government regarding stand- 
ards issued by NBS pursuant to the Federal Property 
and Administrative Services Act of 1949 as amended, 
Public Law 89-306 (79 Stat. 1127), and as implemented 
by Executive Order 11717 (38 FR 12315, dated May 11, 
1973) and Part 6 of Title 15 CFR (Code of Federal 
Regulations). 

NBS Interagency Reports (NBSIR) — A special series of 
interim or final reports on work performed by NBS for 
outside sponsors (both government and non-govern- 
ment). In general, initial distribution is handled by the 
sponsor; public distribution is by the National Techni- 
cal Information Services (Springfield, Va. 22161) in 
paper copy or microfiche form. 



BIBLIOGRAPHIC SUBSCRIPTION SERVICES 



The following current-awareness and literature-survey 
bibliographies are issued periodically by the Bureau: 
Cryogenic Data Center Current Awareness Service. A 

literature survey issued biweekly. Annual subscrip- 
tion: Domestic, $20.00; Foreign, $25.00. 
Liquified Natural Gas. A literature survey issued quar- 
terly. Annual subscription: $20.00. 



Superconducting Devices and Materials. A literature 
survey issued quarterly. Annual subscription: $20.00. 
Send subscription orders and remittances for the pre- 
ceding bibliographic services to National Bureau of 
Standards, Cryogenic Data Center (275.02) Boulder, 
Colorado 80302. 



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